1. ILC-BDS Collimator Study Adriana Bungau and Roger Barlow The University of Manchester CERN - October 15

2. Since last time… Only higher order mode geometric wakefields were implemented in the Merlin code at the last COLSIM meeting Resistive wakefields were included in the simulations (benchmark with an experiment at SLC) At PAC - 07: the increase in the bunch size and the decrease in the luminosity due to geometric and resistive wakefields were presented for large offsets However, large offsets of couple of hundreds of microns are not realistic in a real machine but useful in theory when tried to find the range when the split into modes occurs Small offsets of several sigmas are more likely to happen Beam jitter in all ILC_BDS collimators Wakefield tests at SLAC in March and July (see Jonny’s talk)

3. NoNo NameTypeZ (m)Apertur e 1CEBSY1Ecollimator37.26 ~ 2CEBSY2Ecollimator56.06 ~ 3CEBSY3Ecollimator75.86 ~ 4CEBSY E Rcollimator431.41 ~ 5SP1Rcollimator1066.61x99y99 6AB2Rcollimator1165.65x4y4 7SP2Rcollimator 1165.66x1.8y1.0 8PC1Ecollimator1229.52x6y6 9AB3Rcollimator1264.28x4y4 10SP3Rcollimator1264.29x99y99 11PC2Ecollimator1295.61x6y6 12PC3Ecollimator1351.73x6y6 13AB4Rcollimator1362.90x4y4 14SP4Rcollimator1362.91x1.4y1.0 15PC4Ecollimator1370.64x6y6 16PC5Ecollimator1407.90x6y6 17AB5Rcollimator1449.83x4y4 NoNameTypeZ (m)Aperture 18SP5Rcollimat or 1449.84x99y99 19PC6Ecollimat or 1491.52x6y6 20PDUMPEcollimat or 1530.72x4y4 21PC7Ecollimat or 1641.42x120y10 22SPEXRcollimat or 1658.54x2.0y1.6 23PC8Ecollimat or 1673.22x6y6 24PC9Ecollimat or 1724.92x6y6 25PC10Ecollimat or 1774.12x6y6 26ABEEcollimat or 1823.21x4y4 27PC11Ecollimat or 1862.52x6y6 28AB10Rcollimat or 2105.21x14y14 29AB9Rcollimat or 2125.91x20y9 30AB7Rcollimat or 2199.91x8.8y3.2 31MSK1Rcollimat or 2599.22x15.6y8.0 32MSKCRABEcollimat or 2633.52x21y21 33MSK2Rcollimat or 2637.76x14.8y9 ILC-BDS colimators

4. Bunch size - geometric wakefields - beam parameters at the end of linac:  x = 30.4 10 -6 m,  y = 0.9 10 -6 m - beam size at the IP in absence of wakefields:  x = 6.51*10 -7 m,  y = 5.69*10 -9 m - last talk->modes separation at 250 um (on logarithmic scale!); - for small offsets, modes separation occurs at ~10 sigmas;

5. Luminosity - geometric wakefields - at 10 sigmas when the separation into modes occurs, the luminosity is reduced to 20% - for a luminosity of L~10 38 the offset should be 2-3 sigmas

6. Resistive wall pipe wall has infinite thickness; it is smooth; it is not perfectly conducting the beam is rigid and it moves with c; test charge at a relative fixed distance; b c c The fields are excited as the beam interacts with the resistive wall surroundings; For higher moments, it generates different wakefield patterns; they are fixed and move down the pipe with the phase velocity c;

7. General form of the resistive wake Write down Maxwell’s eq in cylindrical coordinates Combined linearly into eq for the Lorentz force components and the magnetic field Assumption: the boundary is axially symmetric ( are ~ cos mθ and are ~ sin mθ ) Integrate the force through a distance of interest L Apply the Panofsky-Wenzel theorem

8. The MERLIN code Previously in Merlin: Two base classes: WakeFieldProcess and WakePotentials - transverse wakefields - longitudinal wakefields Geometrical wakes: Some functions made virtual in the base classes Two derived classes: - SpoilerWakeFieldProcess - does the summations - SpoilerWakePotentials - provides prototypes for W(m,s) functions (virtual) The actual form of W(m,s) for a collimator type is provided in a class derived from SpoilerWakePotentials WakeFieldProcess WakePotentials SpoilerWakeFieldProcess CalculateCm(); CalculateSm(); CalculateWakeT(); CalculateWakeL(); ApplyWakefield (); SpoilerWakePotentials nmodes; virtual Wtrans(s,m); virtual Wlong(s,m);

9. Implementation of the Resistive wakes WakeFieldProcess WakePotentials SpoilerWakeFieldProcess CalculateCm(); CalculateSm(); CalculateWakeT(); CalculateWakeL(); ApplyWakefield (); SpoilerWakePotentials nmodes; virtual Wtrans(s,m); virtual Wlong(s,m); ResistiveWakePotentials Modes; Conductivity; pipeRadius; Wtrans(z,m,AccComp); Wlong(z,m, AccComp);

10. Resistive wakes Benchmark against an SLC result

11. Bunch size - resistive wakefields For small offsets the mode separation starts at ~10 sigmas At larger offsets (30-35 sigmas) there are particles lost in the last collimators The increase in the bunch size due to resistive wakefields is far greater than in the geometric case

12. Luminosity - resistive wakes - at 10 sigmas when the separation into modes occurs, the luminosity is reduced to 10% - for a luminosity of L~10 38 the offset should be less than 1 sigma - the resistive effects are dominant!

13. Bunch Shape Distortion The bunch shape changes as it passes through the collimator; the gaussian bunch is distorted in the last collimators But the bunch shape at the end of the linac is not a gaussian so we expect the luminosity to be even lower than predicted

14. Beam offset in each BDS collimator No wakefields =4.74e-12; Jitter of 1 nm of maximum tolerable bunch-to-bunch jitter in the train with 300 nm between bunches; for 1nm: =8.61e-11 Jitter about 100 nm which intratrain ffedback can follow with time constant of ~100 bunches; for 100nm: =5.4e-10 Maximum beam offset is 1 um in collimator AB7 for 1nm beam jitter and 9um for 100 nm jitter

15. Beam jitter Beam jitter of 500 nm of train-to-train offset which intratrain feedback can comfortably capture The maximum beam offset in a collimator is 40 um (collimator AB7) for a 500nm beam jitter For 500nm: =2.37e-9

16. Next plans Study the wakefields of one collimator for the material damage tests in Japan (Ti coated with Be - emittance dilution and performance with Ti and Be resistivity) Merlin code development for implementation of ECHO/GDFIDL results …other suggestions?